Variation of the Hausdorff dimension of limits set and degenerating Schottky groups

In this talk, based on a joint work with Vlerë Mehmeti, I will explain how one can use some techniques in non-Archimedean geometry to study families of degenerating complex Schottky groups. More precisely, each Schottky group comes with a fractal set, obtained as a limit of an orbit, called the limit set. We show that under specific conditions, one can obtain an asymptotic formula for the Hausdorff dimension of the limit set. If time permits, I will present how certain functions called Poincare series have very special behavior when one works over non-Archimedean fields.